Third Capra Meeting on Radiation Reaction

Eric Poisson, University of Guelph
poisson@physics.uoguelph.ca
The Capra series of meetings on radiation reaction in curved spacetime were initiated in 1998 by Patrick Brady. The first meeting was held at Frank Capra's ranch in southern California, and the name stayed, even though the location of the meeting has changed. (Frank Capra is the famous movie director who made such films as ``It's a wonderful life'' and ``Mr. Deeds goes to town''. Capra had studied at Caltech before going to Hollywood; he bequeathed his ranch to his alma mater, which passed to Caltech upon his death.) The second meeting was held in Dublin, Ireland, and was organized by Adrian Ottewill. This latest installment was held at Caltech June 5-9, 2000, and was organized by Lior Burko and Scott Hughes. Here I will present a rather broad overview of the main issues discussed during the meeting, and highlight just a few of the contributions. The complete proceedings -- a copy of the slides presented by all the speakers -- can be found at the meetings's web site: http://www.tapir.caltech.edu/~capra3/. This series of meetings is concerned with the motion of a small mass in a strong gravitational field. It is known that in the limit of vanishing mass, the particle moves on a geodesic of the background spacetime. Away from this limit, however, the motion in the background is no longer geodesic, and can be described in terms of a self-force. (In some sense, the motion is geodesic in the perturbed spacetime, which consists of the background plus the perturbation created by the particle. For a point particle, however, the perturbation is singular at the particle's location, and careful thought must be given to the removal of the singular part of the field, which does not affect the motion. In flat spacetime, this subtraction gives rise to the well-known half-retarded minus half-advanced potential.) The main focus of the meeting was the practical computation of this force. While this problem raises many interesting issues of principle (such as the removal of the singular part of the metric perturbation created by a point particle), there is also a practical necessity. The detailed modeling of gravitational waves produced by a solar-mass compact object orbiting a massive black hole requires an accurate representation of the orbital motion, which evolves as a result of radiation loss. In the generic case involving a rapidly rotating black hole, this evolution must be calculated on the basis of a radiation-reaction force. Such sources of gravitational waves will be relevant for the Laser Interferometer Space Antenna (LISA), a space-borne detector designed to measure low-frequency waves (it has a peak sensitivity at around 1 mHz). The electromagnetic analogue to this problem was solved in 1960 by DeWitt and Brehme [1], who derived a curved-spacetime expression for the self-force acting on a point electric charge. The gravitational self-force was obtained much more recently, first by Mino, Tanaka, and Sasaki [2], and then by Quinn and Wald [3]. There is also a similar force in the case of scalar radiation, which was calculated by Quinn [4]. In all three cases the self-force is expressed as an integral over the past world-line of the particle, and the integral involves the nonsingular part of the retarded Green's function, which has support inside the past light cone of the particle's current position. The explicit evaluation of only this part of the Green's function is challenging, however, and a good portion of the meeting was devoted to this issue. A plausible method for calculating the Green's function involves a separation-of-variable approach made possible by the symmetries of the black-hole spacetime. (Thus far, all calculations have been restricted to the case of a Schwarzschild black hole). It is a simple matter to derive and solve the ordinary differential equation that governs each mode of the Green's function. The problem lies with the fact that the sum over all modes doesn't converge. (This is essentially because the individual modes do not distinguish between the singular and nonsingular parts of the Green's function.) Amos Ori, Leor Barack, and Lio Burko [5] have devised a way of regulating the mode sum, so as to extract something meaningful. Their results for simple situations involving scalar radiation were presented at the meeting, and are extremely promising. A similar regularization method was used by Carlos Lousto [6], who calculated the gravitational self-force acting on a radially infalling particle in Schwarzschild spacetime. Regularization was also exploited by Hiroyuki Nakano and Yasushi Mino to calculate the gravitational self-force in the weak-field limit. Insight into the self-force problem can be gained by adopting a more local point of view, and focusing on the immediate vicinity of the particle. Such an approach permits a clear identification of the singular part of the particle's field, which can then be decomposed into modes and subtracted from the full field. Such a strategy was adopted by Steve Detweiler (in the gravitational case) and by Patrick Brady (in the scalar case). A variation on this theme is to start with the Mino et al. expression for the gravitational self-force [2], and to evaluate the contribution to the world-line integral that comes from the particle's very recent past. Results along those lines were presented by Warren Anderson. The third Capra meeting has shown that the radiation-reaction problem is progressing very nicely. There are still many issues left to sort out, but it is nice to see that concrete results have now been obtained. I expect that progress will be swift in the coming year, and that the fourth (perhaps last?) meeting will be just as exciting as the preceding ones.

References:

[1] B.S. DeWitt and R.W. Brehme, Ann. Phys. (NY) 9, 220 (1960).

[2] Y. Mino, M. Sasaki, and T. Tanaka, Phys. Rev. D 55, 3457 (1997).

[3] T.C. Quinn and R.M. Wald, Phys. Rev. D 56, 3381 (1997).

[4] T.C. Quinn, gr-qc/0005030.

[5] See, for example, L.M. Burko, Phys. Rev. Lett. 84, 4529 (2000), and L. Barack, gr-qc/0005042.

[6] C.O. Lousto, Phys. Rev. Lett. 84, 5251 (2000).